Closed system cooled covered roll and methods of forming and operating cooled covered roll

ABSTRACT

Roll, method of forming roll and method of operating roll. Roll includes a roll body, a deformable cover coupled to the roll body, a pluggable input, a pluggable output, and a coolant contained within the roll body at least in an amount sufficient for a rimming mode to occur during normal operation of the roll. The present abstract is neither intended to define the invention disclosed in this specification nor intended to limit the scope of the invention in any way.

DISCUSSION OF BACKGROUND INFORMATION

1. Field of the Invention

The present invention is for use in paper machines having rolls covered with roll covers In particular, the roll covers can be made of polymers, e.g., rubbers, polyurethanes, epoxies, thermosets, thermoplastics, etc., and these paper-machine rolls are internally water cooled in the present state-of-the-art.

2. Discussion of Background Information

Roll covers utilized in critical applications of paper machines are generally water-cooled to counter the internal heating of the cover material as it rolls through the nip. In this regard, the thermo-visco-elasticity of typical roll cover materials increase the internal heating of the cover with increasing nip loads, increasing speeds, and increasing cover thickness. Moreover, with everything else being held constant, the internally generated heat increases for materials having lower thermal conductivity, for materials with lower stiffness, i.e., lower storage modulus “E′,” and for materials that have higher “tangent of the phase angle,” i.e., higher “tan δ.” Thus, it is advantageous to constrain, within limits, the internal and interfacial material properties of the roll cover, e.g., fracture toughness, strength, stiffness, wear resistance, etc., and since the properties of the adhesives used to bond the cover to the roll core decrease with increasing temperature, and since the paper machine process needs a roll cover material with stable properties through time and uniform properties in the cross-machine direction in order to process paper with consistent uniformity.

To ensure an even distribution of temperature from the tending (front) end of the roll to the drive (back) end of the roll, different water-cooling systems have been designed and implemented. A goal of these water cooling designs is to achieve uniform cooling of the roll so as to avoid dead spots, i.e., no flow areas. Generally, the various water-cooling systems utilize water flowing through the roll (in the cross-machine direction) during operation. Accordingly, these designs can require, e.g., flow meters to measure and control a prescribed amount of water flow in and out of the roll, and thermometers and temperature recorders to measure the water temperature in and out of the roll. These flow meters, thermometers and temperature recorders need to be maintained properly, and water pressure and air pressure also need to be periodically monitored. Further, the roll must be continually monitored for too much water, not enough water, and plugged exit ports. The water itself needs to be monitored to ensure it is clean, since, if the water supply contains a large amount of minerals, sludge, or other contaminants, periodic opening may be required to check for scale and mud inside the roll. In the known designs, it is also important, and difficult, to maintain a constant inlet temperature all year round, since available stream water used for cooling these paper machine rolls in most mills can vary more than 22° C. depending on the season. While a heat exchanger can ensure constant incoming cooling water temperatures, this requires additional expenses (including increased energy consumption costs) and increases the maintenance issues.

It is further known, the cooling water in the roll should not be too cold because, if the inside temperature of the cover is significantly cooler than its outside temperature, thermal-gradient-driven permeation may result in debonding of the cover from the roll. This debonding can be caused by condensation of water (driven by permeation through the polymer) at the colder interface. Diffusion of water through the polymer is particularly important for polyurethane covers, since polyurethane is more water-permeable than most rubber compounds. Thus, the cooling water temperature at the inlet of the roll is prescribed to be higher than 24° C. (in the present state of the art) to prevent water permeation damage and hence maintain cover bond integrity. In rolls of this type, regardless of the polymer cover, it is generally recommended to stop the water flow during a shutdown of even short duration. In this regard, if water continues to enter the roll during a shutdown, the roll may fill with water. This can be particularly problematic when the roll during shutdown is partly filled with water colder than the cover temperature, and the top of the roll is not able to cool down to the same temperature as the cold water. As a result, the colder water will pool, by gravity, to the bottom of the roll, which can create a thermal gradient in the roll, i.e., hotter at the top and colder at the bottom. This thermal gradient will produce bending of the roll, e.g., like a banana, with the center of the roll protruding up, i.e., the convex side at the top and the concave side at the bottom. Upon start-up of this distorted roll, non-uniform cross-machine direction contact (and nip pressure profile problems) occurs at the nip, and severe vibrations may arise depending on the severity of the (thermally) bent roll shape.

Therefore, as use of water flowing through a roll to control the heat generation of a cover can create a number of problems and additional costs, it is not surprising that paper mills prefer a roll cover that does not require water flow through the roll to operate. Moreover, the elimination of flow through rolls likewise eliminates the above-noted energy costs, maintenance and operational problems associated with cooling by internal water flow forced through the roll.

The motion of a film of liquid on the inside surface of a roll rotating at a steady rotational speed exhibits a variety of surprisingly profuse flow phenomena. The flow of liquid inside the roll may display various free-surface fluid flow instabilities, pattern formation, non-uniqueness and even non-existence of steady-state fluid flow solutions. The external forces on the fluid film during operation of the roll can include inertia (e.g., centrifugal and Coriolis forces), gravity, viscosity, and surface tension.

At zero rotational speed, the fluid within a partially filled roll is stationary and lies in a pool at the bottom of the roll, and, even at a low speed roll rotation, a liquid film generally lies at the bottom of the partially filled roll, except for a very small amount that travels around with, and wets, the inner wall of the roll. This liquid pool on the bottom of the roll can establish a cellular circulation pattern in the cross-machine or axial direction of the roll. The liquid surface can establish a periodic bore between the liquid and the descending surface of the roll.

As the rotation rate is increased, the surface becomes irregular and can mask this initial periodic pattern. As the fluid film that clings to the surface enters the bottom pool on the receding side, i.e., on the downwardly rotating side of the roll, a sharp straight front is created. An accompanying recirculation region is also formed in the pool that grows in the circumferential direction with increasing rotational speed and the front on the receding side is pulled farther towards the rising side.

With increasing angular speed, the film pulled out of the pool also thickens. The fluid film eventually becomes unstable and the fluid motion changes to a sloshing motion on the rising side of the roll. This falling wave is initially straight in the cross-machine direction of the roll, but at higher rotational speed it breaks up into a number of separate (in the cross-machine direction) gravity waves with approximately parabolic shapes. For a limited range of rotational speed, these gravity waves, sometimes referred to as “pendants,” are practically stationary. At still faster rotational speed, this sloshing instability is overcome by viscosity and the cascading flow becomes essentially two-dimensional.

At high rotational speeds, the front is pulled over the top of the roll, and a “rimming mode” develops where centrifugal forces dominate the flow and the fluid coats the inside surface of the roll. At still higher speeds, and for small enough fill rate of the roll, the fluid coats the inside surface of the roll uniformly and rotates rigidly with the roll. The rotational speed at which the fluid just enters the rimming mode (with increasing rotational speed) is higher than the rotational speed at which the fluid leaves the rimming mode (with decreasing rotational speed). This hysteresis is more pronounced with increasing filling fractions (volume occupied by fluid divided by the total volume inside the roll). Other phenomena associated with the transition regions include the popping or fluttering of surface features associated with strong localized vortex flows inside the fluid sheet, air entrainment at the front, which may lead to avalanches, and shedding of hydroplaning drops. For large filling fractions, curtains or so-called “hygrocysts” spanning the entire cross-machine direction of the roll are formed. For a fluid with small values of viscosity, the flow inside the pool and the rising sheet becomes strongly turbulent. Further, large-scale patterns can persist even in the presence of this (small-scale) turbulent flow.

Therefore, it is known the flow of a homogeneous liquid in the interior of a rotating roll can display a number of different characteristic flow states with various degrees of complexity, including flows that are 3-dimensional with secondary flows in the cross-machine direction of the roll. Moreover, flow states inside rotating rolls have been referred as “flat-front state,” “wavy-front state,” “localized u-shaped structures,” “shark-tooth pattern,” “hydrocysts,” and “cascades.”

For constant kinematic viscosity, the filling fraction level and the rotational speed of the roll are the main determinants of the flow state adopted. For each filling level, the transition between flow states occurs at well defined associated critical rotational speeds. However, the sequence of transition scenarios is not unique, i.e., different transition scenarios can be observed at different locations in the phase plane.

SUMMARY OF THE INVENTION

The present invention targets a roll in a paper machine provided with a roll cover. The roll operates as a closed system, i.e., without the need for fluid flowing into and out of the roll.

Moreover, the roll according to the invention can include an amount of coolant, e.g., water, to provide a thickness of fluid in the operating roll greater than in a rimming mode. According to the invention, this greater than rimming thickness of coolant provides cooling in the longitudinal direction of the roll not achievable by a roll, in particular, a closed roll, operating in the rimming mode.

Further, the present invention exploits the fluid instabilities occurring when a fluid is inside a rotating roll, and in particular, exploits secondary flows in the cross-machine or axial direction, to promote the heat transfer of internally generated heat from the roll cover by fluid convection in the axial direction of the roll.

The invention targets a roll including a roll body, a deformable cover coupled to the roll body, a pluggable input, and a coolant contained within the roll body at least in an amount to provide cross-machine direction heat transfer during normal operation of the roll.

According to a feature of the invention, the roll can be a cooled roll operable as a closed system.

In accordance with another feature, the at least an amount of coolant to provide cross-machine direction heat transfer can include an amount greater than the amount of coolant sufficient for at least a rimming mode to occur.

According to still another feature of the present invention, the at least an amount of coolant to provide cross-machine direction heat-transfer may be determined by the difference in steady state power between operation of the roll with fluid flowing through the input and output of the roll and operation of the roll without coolant.

Further, the at least an amount of coolant to provide cross-machine direction heat-transfer can provide a volume fraction of greater than or equal to 1%. The volume fraction may include a volume of the coolant inside the roll divided by the total inner volume of the roll body.

According to a further feature of the present invention, the roll may further include a siphon with a siphon pick-up shoe positioned near an inner surface of the roll body, and the at least an amount of coolant film thickness to provide cross-machine direction heat-transfer can be greater than or equal to the distance between the inner surface of the roll body and the tip of the siphon pick-up shoe.

In accordance with another feature, the at least an amount of coolant to provide cross-machine direction heat-transfer is determined by the following equation:

Δ≧(¼)(πD ₀ ² L)[1−(2/D ₀)(t _(c) +t _(s))]²{1−{1−[(V/D ₀ ^(0.539))[ν^(0.026)/(6.263 g^(0.513))]* [1−(2/D ₀)(t _(c) +t _(s))]^(0.461)]^(1/0.339)}²},

Where: Δ [m³] represents the fluid volume in the roll body

-   -   D₀ [m] represents the outer diameter of the covered roll;     -   L [m] represents the length of the internal cavity inside the         roll body;     -   t_(c) [m] represents the total cover thickness;     -   t_(s) [m] represents the roll shell thickness of the roll body;     -   V [m/sec] represents the surface speed of the covered roll;     -   ν [m²/sec] represents the dynamic viscosity of coolant; and     -   g [m/sec²] represents the standard acceleration of gravity         (9.80665 m/sec²).

The invention is directed to a method for forming a cooled roll composed of a single shell covered roll having an open internal cavity. The method includes adding coolant into the internal cavity at least in an amount to provide cross-machine direction heat transfer during normal operation of the roll, and plugging a pluggable input of the roll.

According to a feature of the present invention, the at least an amount of added coolant can be an amount greater than the amount of coolant sufficient for at least the rimming mode to occur.

In accordance with another feature of the invention, before the adding of coolant, the method can further include determining a steady state power for operating in the rimming mode with fluid flowing through the roll, determining a steady state power for operating the roll without coolant, and determining the difference in steady state power between operation of the roll with fluid flowing through the roll and operation of the roll without coolant (or with a significantly smaller amount of coolant). The at least an amount of added coolant to be added to the empty cavity can be found when steady state power to the roll with the added amount is at least equal to the determined difference in steady state power.

Moreover, the at least an amount of added coolant can provide a volume fraction of greater than or equal to 1%. The volume fraction may include a volume of the coolant inside the roll divided by a total inner volume of the roll body.

According to another feature of the invention, the roll may further include a siphon with a siphon pick-up shoe positioned near an inner surface of the roll body, and the at least an amount of added coolant film thickness to provide cross-machine direction heat-transfer may be greater than or equal to the distance between the inner surface of the roll body and the tip of the siphon pick-up shoe.

In accordance with still another feature of the present invention, the at least an amount of added coolant can be determined by the following equation:

Δ≧(¼)(πD ₀ ² L)[1−(2/D ₀)(t _(c) +t _(s))]²{1−{1−[(V/D ₀ ^(0.539))[ν^(0.026)/(6.263 g^(0.513))]* [1−(2/D ₀)(t _(c) +t _(s))]^(0.461)]^(1/0.339)}²},

Where: Δ [m³] represents the fluid volume in the roll body

-   -   D₀ [m] represents the outer diameter of the covered roll;     -   L [m] represents the length of the internal cavity inside the         roll body;     -   t_(c) [m] represents the total cover thickness;     -   t_(s) [m] represents the roll shell thickness of the roll body;     -   V [m/sec] represents the surface speed of the covered roll;     -   ν [m²/sec] represents the dynamic viscosity of coolant; and     -   g [m/sec²] represents the standard acceleration of gravity         (9.80665 m/sec²).

According to a still further feature of this invention, the cooled roll may be operated as a closed system.

The invention provides a method for operating a roll of a paper machine composed of a single shell covered roll having an open internal cavity. The method includes adding an amount of coolant into the internal cavity in an amount greater than an amount for operating in a rimming mode during normal operation of the roll, plugging a pluggable input of the roll, and rotating the roll.

In accordance with a feature of the invention, the roll can include a roll cover and the coolant may cool heat internally generated by deformation of the roll cover.

According to another feature of the present invention, rotation of the roll can provide cooling in a machine direction and in a cross-machine direction.

In accordance with still yet another feature of the present invention, the coolant can have a dynamic viscosity of less than 10⁻⁵ m²/sec.

Other exemplary embodiments and advantages of the present invention may be ascertained by reviewing the present disclosure and the accompanying drawing.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is further described in the detailed description which follows, in reference to the noted drawings by way of non-limiting examples of exemplary embodiments of the present invention, in which like reference numerals represent similar parts throughout the several views of the drawings, and wherein:

FIG. 1 illustrates a roll in accordance with the invention; and

FIG. 2 illustrates a siphon roll in accordance with the invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The particulars shown herein are by way of example and for purposes of illustrative discussion of the embodiments of the present invention only and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the present invention. In this regard, no attempt is made to show structural details of the present invention in more detail than is necessary for the fundamental understanding of the present invention, the description taken with the drawings making apparent to those skilled in the art how the several forms of the present invention may be embodied in practice.

The article “Heat Transfer in Single and Double Shell Cooling Rolls,” Industrial and Engineering Chemistry Process Design and Development, Vol. 1, No. 1, pp. 41-45 (January 1962) by Chatterjee et al. is relevant to internal water cooling of rolls. The authors reported on an experimental study of heat transfer of externally-heated single (conventional) and double shell rolls that were internally water-cooled to calender polymer films. The conventional single shell roll has a single unrestricted cavity within which cooling water passes through in the cross-machine direction at relatively low velocity, which the authors noted “is commonly considered the least efficient roll, having the widest variation of surface temperature, probably because of the low heat transfer coefficient of stagnant water in the roll ends.” However, the results of the tests by Chatterjee et al. found that the double shell roll does not, contrary to conventional wisdom, have better heat removal capacity than the single shell roll. Their results also found the highest coefficient of heat transfer occurs at the highest rotational speed and at the lowest flow rate through the roll, and the highest coefficient of heat transfer achieved for the double shell roll is lower than that achieved for the single shell roll. The article by Chatterjee et al. presented their findings, but did not attempt to explain these counter-intuitive results.

The inventor has found, at constant rotational speeds, i.e., high enough such that the centrifugal forces exceed the gravitational forces on the water, the average coefficient of heat transfer decreases with increasing axial flow speed of cooling water. Thus, the axial flow rate disturbs the vortex formation and may actually decrease the heat transfer rate. The inventor has surmised the double shell roll precludes the formation of vortices and general hydrodynamic instability in comparison with the fluid film in a single shell roll that has a free surface that makes it more unstable than the fluid flow in the filled annulus of a double shell. Moreover, the fluid flow inside a double shell roll is constrained by the dimensions of the annulus cavity, while the fluid inside the single shell roll is not so constrained.

Accordingly, FIG. 1 illustrates a roll 1, e.g., a single shell roll with a free interior space, having a roll cover 2, e.g., formed of a polymer such as rubber, polyurethane, etc. Roll 1 can be of conventional design for a roll having a flow F of coolant from a tender or front end 3 to a drive or back end 4. The coolant preferably can be e.g., water or water and ethylene glycol, can have a dynamic viscosity (ν), e.g., lower than 10⁻⁵ m²/sec, and can have a temperature, e.g., between 70° C. and 80° C. Moreover, tender end 3 can include a number of inlets, e.g., four inlets, and drive end 4 can include a number of outlets, e.g., four outlets.

When operated conventionally, the roll is rotated to a rimming mode if the water film is thin enough such that the centrifugal forces dominate the flow and the fluid coats the inside surface of the roll. Further, as these conventional rolls operate with a fluid flow through the roll, the water/coolant moves along the inside surface of roll 1 from tender end 3 to drive end 4. However, as discussed above, when operated conventionally as a flow through coolant, maintenance and operational problems associated with cooling by internal water flow forced through the roll arise to ensure water flow is sufficient to maintain the desired rimming mode.

Roll 1, according to the invention, is operated without the need for fluid flowing through the roll, i.e., from input to output, thereby eliminating the maintenance and operational problems associated with the conventional forced fluid cooling. However, according to a first non-limiting embodiment of the invention, roll 1, operated as a closed system, can be partially filled with an amount of coolant in such an amount that the extra power required to drive the partially filled roll, i.e., as compared to driving roll 1 emptied of fluid, is greater than or equal to the extra amount of power required to drive roll 1 operated as a conventional fluid cooling flowing through the roll. Further, in order to maintain the closed system within roll 1, the output(s) of roll 1 can be plugged prior to partially filling the cavity of roll 1 and the input(s) of roll 1 can be plugged after partially filling the cavity with the amount of coolant to satisfy the features of the invention.

According to the invention, the amount of coolant to be supplied into roll 1, to operate as a closed system, can be determined in the following exemplary manner. Roll 1, operating as a conventional forced fluid cooling roll, can be driven by drive 5 to its normal operating speed with fluid flow within roll 1. The steady state power required to drive the conventional operation of roll 1 at operating speed with flowing fluid is recorded, stored, or identified in some manner by monitoring device 6.

Thereafter, roll 1 can be drained of coolant, and roll 1 can again be driven by drive 5 to normal operating speed. The steady state power necessary to drive the empty roll 1 is likewise recorded, stored, or identified in some manner by monitoring device 6, and a difference between the power required for operating roll 1 in its conventional manner and the power required for operating empty roll 1 is determined. This determined difference in the steady state power to drive roll 1 can then be utilized as a base line for determining the amount of coolant to be added to roll 1 for operation as a closed system. In particular, the outlet of roll 1 is plugged, and coolant is added to partially fill roll 1 until the amount of power required to drive the partially filled roll at steady state conditions at least equals, and preferably is greater than, the steady state power required to drive the roll with conventional cooling fluid flowing in and out through roll 1. The inlet can then be plugged so roll 1 can be operated as a closed system.

In this manner, the coolant film within roll 1 is thick enough to prevent rimming during normal operation, thereby providing sufficient coolant within roll 1 to operate as a closed system with cooling provided even in the longitudinal direction. Thus, in contrast to known systems, the present invention provides cross-machine convection heat transfer as well as machine direction heat transfer.

In an alternative embodiment, the amount of coolant loaded into roll 1 to operate as a closed system can be determined by interior volume of roll 1. By way of non-limiting example, paper machine roll 1 can be filled with an amount of fluid/coolant such the volume fraction, i.e., the volume of fluid inside roll 1 divided by the total interior volume of the empty cavity of roll 1, is at least equal to, and preferably greater than, 1%.

In accordance with the exemplary embodiment of FIG. 1, it is understood existing conventional flow through coolant rolls can be retrofit to operate as a closed system, in accordance with the features of the invention. By way of a further non-limiting embodiment, FIG. 2 shows a conventional siphon roll 10, e.g., a Voith Siphon Roll, having a fluid or coolant injector nozzle 11 to supply coolant into the interior of roll 10 and toward drive or back end 12. The fluid flow within the interior of roll 10, i.e., when operated conventionally as a coolant flow through roll, goes from drive end 12 toward tender or front end 13. Further, a siphon 14 having a pick-up shoe 15 is arranged near tender end 13 to pick up excess fluid within the interior of roll 10 and guide this excess fluid out of roll 10. Further, as with these conventional type rolls, roll 10 is likewise driven at such a speed so as to operate in rimming mode. It is noted water siphons in conventional siphoned rolls are set to a distance between 5 mm and 10 mm, and generally 5 mm, from the interior surface of the roll so the fluid film will be in rimming mode during operation of the siphoned roll.

However, as the present invention is counter to the conventional wisdom of operating in rimming mode, particularly when the roll is operated as a closed system, because rimming prevents cross-direction currents, this embodiment of the present invention utilizes more coolant in the siphon roll operating as a closed system than would be utilized in the siphon roll operating conventionally. Further, as the siphon roll according to the invention operates as a closed system, siphon 14 is not used per se. However, siphon 14, and more particularly, pick-up shoe 15, is utilized to determine the amount of coolant to be loaded into the interior of roll 10. In this regard, by way of non-limiting example, the outlet of roll 10 can be plugged, and the interior of roll 10 can be partially filled with an amount of fluid so the fluid film thickness during operation is greater than or equal to the distance between the interior surface of roll 10 and a tip of pick-up shoe 15 of siphon 14. Thereafter, the roll input can be plugged, and the roll can be operated as a closed system.

In a still further alternative embodiment, the amount of coolant supplied into the roll, e.g., a conventional roll with forced fluid cooling, such as depicted in FIG. 1, intended to operate as a closed system can be determined, by way of non-limiting example, from a volume fraction, i.e., the volume of fluid inside roll 1 divided by the total interior volume of roll 1. While the above-discussed exemplary embodiment partially filled the roll until the volume fraction was greater than or equal to 1%, this exemplary embodiment utilizes the following equations for optimizing the amount of fluid within the closed system roll according to the invention.

An initial determination of the inner volume of the cavity in the roll (ψ [m³]) is made according to the following equation:

ψ=(¼)(πD ₀ ² L)[1−(2/D ₀)(t _(c) +t _(s))]²   (1)

Where: D₀ [m] represents the outer diameter of the covered roll;

-   -   L [m] represents the length of the internal cavity inside the         roll;     -   t_(c) [m] represents the total cover thickness; and     -   t_(s) [m] represents the roll shell thickness.

The following equation can be utilized to solve for fluid volume (Δ [m³]):

Δ=ψ−(¼)(πD ₀ ² L)[1−(2/D ₀)(t _(c) +t _(s) +t _(f))]²   (2)

Where: t_(f) [m] represents fluid film thickness.

Equations (1) and (2) can be utilized to determine the fluid volume fraction (Φ)) based upon the following equation:

Φ=Δ/ψ=1−{1−[(2t _(f) /D ₀)/[1−(2/D ₀)(t _(c) +t _(s))]]}²   (3)

The following equation can be used to determine a minimum fluid film thickness within the roll:

t _(f)≧{(V/D ₀ ^(0.2))[ν^(0.026)/(7.922 g^(0.513))][1−(2/D ₀)(t _(c) +t _(s))]^(0.8)}^(1/0.339)   (4)

Where: V [m/sec] represents the surface speed of the covered roll;

-   -   ν [m²/sec] represents the dynamic viscosity of fluid; and     -   g [m/sec²] represents the standard acceleration of gravity         (9.80665 m/sec²).

A minimum fluid volume fraction can then be determined from the following equation:

Φ≧1−{1−[(V/D ₀ ^(0.539))[ν^(0.026)/(6.263 g^(0.513))][1−(2/D ₀)(t _(c) +t _(s))]^(0.461)]^(1/0.339)}²   (5)

Finally, in order to optimize the amount of fluid within the roll, fluid volume (Δ) is the unknown that is to be solved. A determination of the minimum fluid volume can be calculated from the following equation:

Δ≧(¼)(πD ₀ ² L)[1−(2/D ₀)(t _(c) +t _(s))]²{1−{1−[(V/D ₀ ^(0.539))[ν^(0.026)/(6.263 g^(0.513))]* [1−(2/D ₀)(t _(c) +t _(s))]^(0.461)]^(1/0.339)}²}  (6)

An example of the operation of the above-noted equations according to the invention will now be discussed. Accordingly, if it is assumed the roll has the following:

-   Surface speed of the covered roll (V) is 10.16 m/sec; -   Outer diameter of covered roll (D₀) is 1.5113 m; -   Length of internal cavity inside roll (L) is 8.2931 m; -   Total Cover Thickness (t_(c)) is 0.01905 m; -   Roll Shell Thickness (t_(s)) is 0.06731 m; -   Dynamic Viscosity of fluid (ν) is 0.00000375 m²/sec; -   Standard acceleration of gravity (g) is 9.80665 m/sec².

From equation (1), the inner volume of the cavity inside the roll (ψ) is calculated as 11.67066 m³. Moreover, it follows that, from a roll having this inner cavity volume, the remaining parameters of the roll can be optimized in accordance with the invention. Thus, from equation (4), the minimum fluid film thickness t_(f) can be calculated as t_(f)≧0.014858 m, a minimum fluid volume fraction (Φ) can be calculated from equation (5) as Φ≧4.39%, and a minimum fluid volume (Δ) can be calculated as Δ≧0.5124 m³=512.4 liters.

It is noted that the foregoing examples have been provided merely for the purpose of explanation and are in no way to be construed as limiting of the present invention. While the present invention has been described with reference to an exemplary embodiment, it is understood that the words which have been used herein are words of description and illustration, rather than words of limitation. Changes may be made, within the purview of the appended claims, as presently stated and as amended, without departing from the scope and spirit of the present invention in its aspects. Although the present invention has been described herein with reference to particular means, materials and embodiments, the present invention is not intended to be limited to the particulars disclosed herein; rather, the present invention extends to all functionally equivalent structures, methods and uses, such as are within the scope of the appended claims. 

1. A roll comprising: a roll body; a deformable cover coupled to the roll body; at least one pluggable input; and a coolant contained within the roll body at least in an amount to provide cross-machine direction heat transfer during normal operation of the roll.
 2. The roll in accordance with claim 1, wherein the roll is a cooled roll operable as a closed system.
 3. The roll in accordance with claim 1, wherein the at least an amount of coolant to provide cross-machine direction heat transfer comprises an amount greater than an amount of coolant sufficient for at least a rimming mode to occur.
 4. The roll in accordance with claim 1, wherein the at least an amount of coolant to provide cross-machine direction heat transfer is determined by a difference in steady state power between operation of the roll with fluid flowing through the input and output of the roll and operation of the roll without coolant.
 5. The roll in accordance with claim 1, wherein the at least an amount of coolant to provide cross-machine direction heat transfer provides a volume fraction of greater than or equal to 1%.
 6. The roll in accordance with claim 5, wherein the volume fraction comprises a volume of the coolant inside the roll divided by a total inner volume of the roll body.
 7. The roll in accordance with claim 1, further comprising a siphon with a siphon pick-up shoe positioned near an inner surface of the roll body, wherein the at least an amount of coolant to provide cross-machine direction heat transfer is greater than or equal to a distance between the inner surface of the roll body and a tip of the siphon pick-up shoe.
 8. The roll in accordance with claim 1, wherein the at least an amount of coolant to provide cross-machine direction heat transfer is determined by the following equation: Where: Δ [m³] represents the fluid volume in the roll body D₀ [m] represents the outer diameter of the covered roll; L [m] represents the length of the internal cavity inside the roll body; t_(c) [m] represents the total cover thickness; t_(s) [m] represents the roll shell thickness of the roll body; V [m/sec] represents the surface speed of the covered roll; ν [m²/sec] represents the dynamic viscosity of coolant; and g [m/sec²] represents the standard acceleration of gravity (9.80665 m/sec².).
 9. A method for forming a cooled roll composed of a single shell covered roll having an open internal cavity, comprising: adding coolant into the internal cavity at least in an amount to provide cross-machine direction heat transfer during normal operation of the roll; and plugging a pluggable input of the roll.
 10. The method in accordance with claim 9, wherein the at least an amount of added coolant comprises an amount greater than an amount of coolant sufficient for at least a rimming mode to occur.
 11. The method in accordance with claim 9, wherein, before the adding of coolant, the method further comprises: determining a steady state power for operating with fluid flowing through the roll; determining a steady state power for operating the roll without coolant; and determining the difference in steady state power between operation of the roll with fluid flowing through the roll and operation of the roll without coolant, wherein the at least an amount of coolant added to the cavity is found when steady state power to the roll with the added amount is at least equal to the determined difference in steady state power.
 12. The method in accordance with claim 9, wherein the at least an amount of added coolant provides a volume fraction of greater than or equal to 1%.
 13. The method in accordance with claim 12, wherein the volume fraction comprises a volume of the coolant inside the roll divided by a total inner volume of the roll body.
 14. The method in accordance with claim 9, wherein the roll is further composed of a siphon with a siphon pick-up shoe positioned near an inner surface of the roll body, and wherein the at least an amount of added coolant is greater than or equal to a distance between the inner surface of the roll body and a tip of the siphon pick-up shoe.
 15. The method in accordance with claim 9, wherein the at least an amount of added coolant is determined by the following equation: Where: Δ [m³] represents the fluid volume in the roll body D₀ [m] represents the outer diameter of the covered roll; L [m] represents the length of the internal cavity inside the roll body; t_(c) [m] represents the total cover thickness; t_(s) [m] represents the roll shell thickness of the roll body; V [m/sec] represents the surface speed of the covered roll; ν [m²/sec] represents the dynamic viscosity of coolant; and g [m/sec²] represents the standard acceleration of gravity (9.80665 m/sec²).
 16. The method in accordance with claim 9, wherein the cooled roll is operated as a closed system.
 17. A method for operating a roll of a paper machine composed of a single shell covered roll having an open internal cavity, comprising: adding an amount of coolant into the internal cavity in an amount greater than an amount for operating in a rimming mode during normal operation of the roll; plugging a pluggable input of the roll; and rotating the roll.
 18. The method in accordance with claim 17, wherein the roll includes a roll cover and the coolant cools heat created by deforming the roll cover.
 19. The method in accordance with claim 17, wherein rotation of the roll provides cooling in a machine direction and in a cross-machine direction.
 20. The method in accordance with claim 17, wherein the coolant has a dynamic viscosity of less than 10⁻⁵ m²/sec. 